Since we can't really formally prove most code, I think property based testing such as with hypothesis[1] would make sense. I have not used it yet, but am about to for stuff that really needs to work.
> All of the things you mentioned are designed and tested incrementally.
In a different way that what is proposed in this thread. We don't build a small bridge and grow it. We build small bridges, develop a theory for building bridges and use that to design the big bridge.
I don't know of any theory of computing that would help us design a "big" program at once.
Not saying you're wrong, but I wonder what is the differentiating factor for software? We can build huge things like airliners, massive bridges and buildings without starting small.
Incremental makes less sense to me when you want to go to mars. Would you propose to write the software for such a mission in an incremental fashion too?
Yet for software systems it is sometimes proposed as the best way.